A Decomposition Method for Two stage Stochstic Programming with Block Diagonal Structure

블록 대각 구조를 지닌 2단계 확률계획법의 분해원리

This paper develops a decomposition method for stochastic programming with a block diagonal structure. Here we assume that the right-hand side random vector of each subproblem is differente each other. We first, transform this problem into a master problem, and subproblems in a similar way to Dantizig-Wolfe's Decomposition Princeple, and then solve this master problem by solving subproblems. When we solve a subproblem, we first transform this subproblem to a Deterministic Equivalent Programming (DEF). The form of DEF depends on the type of the random vector of the subproblem. We found the subproblem with finite discrete random vector can be transformed into alinear programming, that with continuous random vector into a convex quadratic programming, and that with random vector of unknown distribution and known mean and variance into a convex nonlinear programming, but the master problem is always a linear programming.